Summer School on Novel Quantum Phases and Non-Equilibrium Phenomena in Cold Atomic Gases. 27 August - 7 September, 2007

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1 Summer School on Novel Quantum Phases and Non-Equilibrium Phenomena in Cold Atomic Gases 27 August - 7 September, 2007 Dipolar BECs with spin degrees of freedom Yuki Kawaguchi Tokyo Institute of Technology

2 Dipolar BECs with Spin Degrees of Freedom YUKI KAWAGUCHI Tokyo Institute of Technology, Japan Collaborators: Hiroki Saito (Univ. of Elec.-Comm., Japan) Masahito Ueda (Tokyo Tech., ERATO-JST, Japan)

3 Outline Introduction : dipole-dipole interaction What's new in a spinor dipolar BEC - Einstein-de Haas effect YK, H. Saito, and M. Ueda, PRL 96, (2006) - Ground-state circulation YK, H. Saito, and M. Ueda, PRL 97, (2006) - Possible experimental scheme YK, H. Saito, and M. Ueda, PRL 98, (2007)

4 Dipole-Dipole Interaction anisotropic long-range tensor force geometry dependence attractive repulsive + spin degrees of freedom spin relaxation spin texture formation?

5 Dipole-Dipole Interaction Magnetic dipole-dipole interaction weak solid-state ferromagnets Electric dipole-dipole interaction

6 Dipole-Dipole Interaction + spin degrees of freedom dipole moment µ dipolar energy V dd energy ratio dd / E con Alkali atom (spin-1) µ B / nk 0.1 % 52 Cr atom 6 µ B 10 nk 10 % 100 % heteronuclear molecule external electric field E 10 µk > 100 % Th. Lahaye et. al., Nature 448, 672 (2007).

7 Polarized Dipolar BEC Stability of the ground state Santos, Shlyapnikov, Zoller and Lewenstein, PRL 85, 1791 (2000) O'Dell, Giovanazzi, and Eberlein, PRL 92, (2004) Collective mode Yi and You, PRA 66, (2002) Goral and Santos, PRA 66, (2002) Optical lattice Supersolid Goral, Santos, and Lewenstein, PRL 88, (2002) Roton-maxon excitation O'Dell, Siovanazzi, and Kurizki, PRL 90, (2003) Santos, Shlyapnikov, and Lewenstein, PRL 90, (2003) Rotating Dipolar BEC Cooper, Rezayi, and Simon, PRL 95, (2005) Zhang and Zhai, PRL 95, (2005) Yi and Pu, PRA 73, (R) (2006) 1D and 2D dipolar gases Pedri and Santos, PRL 95, (2005) H. P. Büchler, et. al., PRL 96, (2007) R. Citro, et. al., PRA 75, (2007)

8 Spinor Dipolar BECs Dipole Ordering in 1D and 2D Mott-Insulator Pu, Zhang, and Meystre, PRL 87, (2001) Gross et. al., PRA 66, (2002) SUPERFLOW Ground State Phase with Single-Mode Approximation Yi, You, and Pu, PRL 93, (2004) Santos and Pfau, PRL 96, (2006) Diener and Ho, PRL 96, (2006) SPIN TEXTURE Spin dinamics in Optical Lattice Sun, Zhang, Chapman, and You, PRL 97, (2006) Molecular BEC in Optical Lattice Barnett, Petrov, Lukin, and Demler, PRL 96, (2006) Micheli, Brennen, and Zoller, Nature Physics 2, 341 (2006)

9 Einstein-de Haas Effect YK, Saito, and Ueda, PRL 96, (2006) See also, Santos & Pfau, PRL 96, (2006) Dipolar interaction B spin SPIN ORBTAL BEC starts rotating mass flow

10 Einstein-de Haas Effect Non-local Gross Pitaevskii equation local density: spin matrix local magnetization: kernel of the dipolar interaction:

11 Einstein-de Haas Effect Non-local Gross Pitaevskii equation Numerical results for a 52 Cr BEC spin-3 : 7-component GP eq. local density: spin matrix local magnetization: kernel of the dipolar interaction: 2 ms

12 Einstein-de Haas Effect Spin relaxation Larmor precession around the dipole field spin mass flow dipole field spin texture

13 What is the ground state of a spinor dipolar BEC???

14 Ground-State Circulation flux-closure constraint solid-state ferromagnets ferromagnetic BEC domain (spin) structure spin texture spin-gauge symmetry mass current then... spontaneous mass current in the ground state??? YES!!!

15 Flux-Closure Constraint Dipolar interaction energy Domain structure in 2D ferromagnets Landau & Lifshitz, Energy of the static magnetic field induced by the magnet source Flux-closure constraint: ferromagnets BEC (no rigid boundary) structure formation flux-closure structure

16 Spin-Gauge Symmetry - ferromagnetic or locally spin-polarized BECs - order parameter (spin 1) superfluid velocity Texture mass current Circulation not quantized Circulation + topological phase quantized

17 Energy Scales high T 1 mk Zeeman 100 mg ln T 100 nk 10 nk 1 nk 0.1 nk spin-independent mean-field interaction + harmonic trap density distribution: spin-exchange interaction magnetism (form of the order parameter) dipolar interaction spin texture low T

18 Characteristic Length Scales spin-indep. mf + trap Thomas-Fermi radius 1~100 µm spin-exchange spin healing length dipole dipole healing length 87 Rb 2 µm 6 µm 52 Cr 0.5 µm 0.6 µm ω : trap frequency n 0 : TF peak n~5x10 14 cm -3 Spin texture can develop when.

19 Phase Diagram - ferromagnetic BEC - YK, Saito, and Ueda, PRL 97, (2006) See also, Yi & Pu, PRL 97, (2006) in a spherical trap

20 Flower Phase almost spin polarized spin texture mass flow

21 Chiral Spin-Vortex Phase chiral symmetry breaking state spin texture mass flow chirality

22 Polar-Core Vortex Phase flux-closure structure spin defect (polar core) polar core spin texture mass flow

23 Phase Diagram 1st order phase transition flux-closure structure 2nd order phase transition chiral symmetry breaking spin-polarized

24 Phase Diagram total angular momentum 0 1st order phase transition flux-closure structure 2nd order phase transition total angular momentum 1 spontaneously rotating state chiral symmetry breaking spin-polarized

25 Ground-State Circulation flux-closure constraint spin texture spin-gauge symmetry ground-state circulation for Rb atoms

26 Dipolar Interaction vs. Zeeman Energy Zeeman : Dipole : Critical field 87 Rb : 52 Cr :

27 Then... is the spinor dipolar effect observable only when the external magnetic field is extremely weak? NO!!! There is an observable effects even though the Zeeman energy dominates the system.

28 Possible Experimental Scheme inhomogeneous dipole field rf-pulse inhomogeneous Larmor precession spin texture YK, H. Saito, and M. Ueda, PRL 98, (2007)

29 Numerical results for 87 Rb BEC

30 Numerical results for 87 Rb BEC TIME SCALE 52 Cr BEC : times faster than 87 Rb BEC - spin texture develops in a few ms

31 Berkeley Experiment J. M. Higbie, et. al., PRL 95, (2005). Observation of the Larmor precession. Phase contrast imaging Time development of homogeneous Larmor precession time rf pulse beat sampling rate : 20 khz Larmor precession : 28 khz

32 Berkeley Experiment J. M. Higbie, et. al., PRL 95, (2005). Observation of the Larmor precession. Phase contrast imaging helical structure Time development of under field gradient time homogeneous Larmor precession rf pulse beat time When helical structure will appear without field gradient sampling rate : 20 khz Larmor precession : 28 khz

33 Summary - Einstein-de Haas effect YK, H. Saito, and M. Ueda, PRL 96, (2006) - Ground-state circulation YK, H. Saito, and M. Ueda, PRL 97, (2006) - Possible experimental scheme YK, H. Saito, and M. Ueda, PRL 98, (2007) Unique feature of a spinor dipolar BEC DIPOLAR : flux-closure constraint SPINOR : spin-gauge symmetry Dipolar BEC becomes more exciting when it has internal degrees of freedom!

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